35 questions

Part 1, Questions 1-5 (50 points)

1. [5] Which ONE of the following is an atomic statement?

[ ] A. Answer the phone when it rings.

[ ] B. Tomorrow will be warm unless it rains.

[ ] C. Mary will get a ticket if she runs the red light.

[ ] D. Today is not his birthday.

[ ] E. Fred visited Jana in the hospital during her recovery

2. [10] Which ONE of the following is true of deductive arguments?

[ ] A. If a valid argument has all false premises, its conclusion must be false.

[ ] B. If a valid argument has a true conclusion, it is sound.

[ ] C. Arguments that are strong and valid have all true premises.

[ ] D. Arguments with contradictory premises are valid.

[ ] E. If there is a counter-example, the argument might be valid but cannot be sound.

3. [10] What is the main operator of the following statement?

If Sarah either studies abroad or moves off campus then both her GPA will drop and she’ll have less fun. [ ] A. Negation [ ] B. Conditional [ ] C. Disjunction [ ] D. Conjunction

Translations

4. [10] Translate the following statement into formal notation. Show any relevant work. Saul will go to campus and return the library books if he picks up his car from the shop or catches the bus.

5. [15] Translate the following argument into formal notation. Show any relevant work.

If Judith qualifies, she will compete in the Olympics or become a professional athlete. But, if Judith doesn’t qualify she will neither compete in the Olympics nor become a professional athlete. Judith will qualify only if she trains all year and hires a coach. Judith will hire a coach. Therefore, if Judith trains all year, she will qualify and either compete in the Olympics or become a professional athlete.

Part 2 (50 points), Questions 6-10

6. [10] An argument must be valid if

[ ] A. its premises are true and its conclusion is consistent with the premises.

[ ] B. its conclusion is a tautology.

[ ] C. its conclusion is a contingency.

[ ] D. its premises strongly support the conclusion.

7. [10] All of the following can be evaluated using a truth table except which one?

[ ] A. Whether two statements jointly imply a third.

[ ] B. Whether two statements are consistent

[ ] C. Whether an argument is cogent.

[ ] D. Whether a statement is a tautology.

8. [10] Which is true?

[ ] A. Any argument with consistent premises is valid

[ ] B. Arguments with contradictory premises are not valid

[ ] C. Any argument with contingent premises is valid

[ ] D. Any argument with a tautological premises is valid

[ ] E. None of the above

Truth Tables

9. [10] Do a truth table for the following statement, and determine whether the statement is a tautology, contradiction or contingency. Explain how you got your answer.

(A v ~B) • (A ⊃ B)

10. [10] Using a truth table, determine whether the following argument is valid. Explain how you get your answer.

1. ~(B v B)

2. B ⊃ A

∴ 3. A

Part 3 (50 points), Questions 11-15

11. [10] All of the following are true of conditional proof except which one:

[ ] A. CP can be used to derive any conditional only if it actually follows from the premises

[ ] B. the antecedent and consequent of the derived conditional don’t need to be atomic statements

[ ] C. to complete a CP you must generate an explicit contradiction

[ ] D. No proof is finished until all subproofs in it are closed

[ ] E. Once a subproof is closed, no individual lines in it can be cited or use

12. [10] Which of the following is a correct application of MP?

[ ]. A

1. A ⊃ B

2. ~A

∴ 3. ~B

[ ] B.

1. (A v B) ⊃ C

2. A

∴ 3. C

[ ] C.

1. A ⊃ (B • C)

2. ~(B • C)

∴ 3. ~A

[ ] D.

1. ~(B • C) ⊃ (A ⊃ D)

2. ~(B • C)

∴ 3. (A ⊃ D)

13. [10] Fill in the lines for the following proof

1. P v D

2. D ⊃ ~S

3. P ⊃ ~K

4. S / ∴ X ⊃ ~K

5. ___________ ACP

6. ___________ 2, 4 MT

7. ___________ 1, 6 DS

8. ___________ 3, 7 MP

9. ___________ 5-8 CP

14. [10] Do the following proof using ONLY INFERENCE RULES (no replacement rules, CP, IP, or optional rules):

1. X ⊃ ~K

2. ~(X v Z) ⊃ ~N

3. K • N / ∴ Z v A

15. [10] Do the following proof using CP and inference rules (no replacement rules, IP, or optional rules).

1. ~(~A • ~N) ⊃ ~(X ⊃ Y)

2. ~X v Y

3. A v B / ∴ B

Part 4 (50 points), Questions 16-20

16. Which one of the following statements is true?

[ ] A. Both inference rules and replacement rules can be applied to parts of a line.

[ ] B. Inference rules only go in one direction, but replacement rules can go in both directions.

[ ] C. Replacement rules only go in one direction, but inference rules can go in both directions.

[ ] D. Inference rules allow one to replace a statement with any other consistent statement.

17. [10] Fill in justifications

1. (A v ~B) ⊃ ~~C

2. ~(C • F)

3. F /∴ ~B ⊃ Y

4. ~C v ~F ___________________

5. ~C ___________________

6. ~(A v ~B) ___________________

7. ~A • B ___________________

8. B ___________________

9. B v Y ___________________

10. ~B ⊃ Y ___________________

18. [10] Do the following proof without using IP, CP, or rules from the optional material.

1. (S • ~T) ⊃ ~R /∴ (R ⊃ T) v ~S

19. [10] Do the following proof using IP

1. A ⊃ (B ⊃ C)

2. B ⊃ (C ⊃ ~B) / ∴ A ⊃ ~B

20. [10] Demonstrate that the following statement

is a tautology using any proof method (NOT a truth

table).

/∴ (X v Y) v [(Y ⊃ ~Y)• ~X]

Part 5 (50 points) Questions 21-25

21. [10] Identify the conclusion of the following argument (don’t worry about whether the argument is good or bad, just figure out what the conclusion being argued for is).

“The most blatant occurrence of recent years is all these knuckleheads running around protesting nuclear power – all these stupid people who do no research at all and who go out and march, pretending they care about the human race, and then go off in their automobiles and kill one another” – Ray Bradbury

[ ] A. People who protest nuclear power are uninformed and disingenuous.

[ ] B. One should not support nuclear power, since it is more dangerous than people think [ ] C. Automobiles should be driven more carefully.

[ ] D. The passage doesn’t contain an argument.

22. [10] The following passage contains TWO fallacies. They are:

[10] I couldn’t believe it when Alex told me that he didn’t think breaking a mirror was bad luck. Everyone knows that breaking a mirror is bad luck. I broke a mirror in high school and something terrible happened the next day. And so now I try to avoid breaking mirrors.

[ ] A. False Cause and Ad Populum Bandwagoning

[ ] B. Tu Quoque and Straw Man

[ ] C. Ad Populum Snobbery and Alternate Description

[ ] D. Ad Hominem Abusive and Slippery Slope

23. [10] If today you can make teaching evolution in public schools a crime, then tomorrow you can make it a crime to teach it in private schools. Then you can ban books and other educational materials that mention evolution. And then you can ban the very word from all discourse. And then the anti-science bigots will have won.

[ ] A. Straw Man

[ ] B. Slippery Slope

[ ] C. Alternate description

[ ] D. False cause

24. [10] You should definitely make caring for your teeth a priority. If you don’t make any attempt to take care of your teeth, then bacteria will build up on your teeth producing a sticky film called plaque. Plaque can cause cavities and gum disease which if left untreated may lead to you losing your teeth.

[ ] A. Ad populum snobbery

[ ] B. Ad populum bandwagoning

[ ] C. False cause

[ ] D. No fallacy

25. [10] Read the passage and answer questions a-d.

Anthony argues that capital punishment should be abolished. But why should we listen to him? He’s a prisoner on death row right now.

a) Does the passage contain an argument? Is there more than one reasonable interpretation of the argument? Note any ambiguities in either case (1-3 sentences)

b) Put the argument into standard form. If there is more than one reasonable interpretation, put both arguments into standard form.

c) Does the argument fit the pattern of any informal fallacies? If so, explain the general form of that fallacy.

d) Determine whether the argument(s) you have identified are in fact fallacious. Explain your answer. (1-3 sentences)

Part 6 (150 points) Questions 26-35

26. [15] Jerry is a big astrology fan who reads his horoscope every week. When his friends tell him that horoscopes are inaccurate, Jerry tells them about the times his horoscope accurately predicted events in his life. Even though his horoscope is wrong more often than right, he continues to plan his life around what it says. Which bias is most likely the primary influence on Jerry’s reasoning?

[ ] A. Zero sum bias

[ ] B. Dunning-Kruger Effect

[ ] C. Confirmation bias

[ ] D. Knobe effect

[ ] E. All of the above

27. [15] A scientific journal publishes research that successfully replicates results from prior experiments, but it does not publish failed attempts to replicate results. People who read the journal often overestimate the replication rate for experiments. Which bias is most likely in play?

[ ] A. Availability Bias

[ ] B. Zero-Sum

[ ] C. Dunning-Kruger effect

[ ] D. Knobe effect

[ ] E. A, B, and C but not D

28. [15] Which of the following is/are forms of the attribution bias?

[ ] A. In an ambiguous encounter, a person who is aggressive is likely to interpret others as expressing aggression.

[ ] B. In ambiguous situations, people with expertise in some domain underestimate their competence.

[ ] C. When something good happens in an ambiguous situation people are more likely to interpret it as the result of an accident than if something bad happens.

[ ] D. A and C, but not B.

[ ] E. All of the above.

29. [15] Someone from Phoenix who watches crime dramas based in New York City on TV overestimates the risk of getting mugged while visiting New York City. Which bias is most likely in play?

[ ] A. Knobe effect

[ ] B. Dunning-Kruger effect

[ ] C. Availability Bias

[ ] D. Confirmation Bias

[ ] E. B and C, but not A or D

30. [15] Which of the following exemplifies the zero-sum bias?

[ ] A. Joe is an only child, and he doesn’t want his parents to have another child because he fears if they do they will love him less.

[ ] B. someone thinks they have a better chance of getting the flu because their friends have the flu. [ ] C. Ann wants to get to the party early because she was told there is a limited amount of cake

[ ] D. someone who applies for a competitive scholarship doesn’t want the other applicants to win.

[ ] E. All of the above.

31. [15] Airbnb allows people to rent out their homes as vacation rentals. People who advertise vacation rentals review personal profiles to choose renters who are trustworthy. African Americans’ and members of other minority groups’ requests for rentals are denied at much higher rates than Caucasians. All of the following biases might plausibly play a role in this except which one?

[ ] A. Confirmation bias

[ ] B. Implicit Race bias

[ ] C. Dunning-Kruger Effect

[ ] D. Availability bias

32. [15] In response to the following passage, 83% of subjects in a study said that the CEO intentionally harmed the environment:

The CEO of a company is sitting in his office when his Vice President of R & D comes in and says ‘We are thinking of starting a new program. It will help us increase profits, and it will also harm the environment.’ The CEO responds that he doesn’t care about harming the environment and just wants to make as much profit as possible. The program is carried out, profits are made and the environment is harmed.

A different set of subjects read a passage identical to the one above except that “harm the environment” was replaced by “help the environment.” Only 23% of them said that the CEO intentionally helped the environment. Which bias do study participants demonstrate?

[ ] A. Dunning-Kruger Effect

[ ] B. Zero sum bias

[ ] C. Knobe Effect

[ ] D. Confirmation Bias

33. [15] Which ONE of the following is true of implicit gender bias?

[ ] A. they are always based on false stereotypes about genetic differences between people. [ ] B. it attributes cultural differences to genetic differences.

[ ] C. women can exhibit gender bias against women.

[ ] D. only people who are overtly sexist exhibit it.

[ ] E. All of the above.

34. [15] Professor Karen Roe, an experienced, expert female physicist, teaches a lower-division course at a university. Her three male teaching assistants Brad, Joe, and Mark are second year PhD students in her department. Despite her greater expertise, students in the class tend to place more trust in the teaching assistants. The teaching assistants respond to their questions confidently, providing definitive answers. By comparison, professor Roe rarely offers simple, straightforward answers. Instead, she responds by discussing multiple possible answers without committing to any of them. Students perceive her as lacking confidence, attributing it to lesser expertise. They often doubt what she says in class, sometimes directing questions to the teaching assistants instead. When their answers conflict, students tend to believe the teaching assistants. Answer the following 2 questions:

Which biases might help explain the behavioral differences (for example, how they answer questions differently) between Professor Roe and her teaching assistants? Explain in 2-3 sentences. (Note that this question is asking which biases might be playing a role. It is not asking about other things that might possibly play a role, such as

whether Roe or the TAs are just objectively better teachers. There may be many factors. In this class we are focusing on biases and the impacts that biases might make.)

Which biases might contribute to the different attitudes students display toward Professor Roe and the TAs? Explain in 2-3 sentences. (Note that this question is asking which biases might be playing a role. It is not asking about other things that might possibly play a role, such as whether Roe or the TAs are just objectively better teachers. There may be many factors. In this class we are focusing on biases and the impacts that biases might make.)

35. [15] Explain two ways that confirmation bias can affect what people believe. Give an example for one of them.

1. [10] Translate the following statement into formal notation.

It is false that having feet is neither necessary nor sufficient for being a mammal.

2. [10] Express the formal statement you got in Optional Question 1 in cDNF

3. [10] Use the proof method to demonstrate that the replacement rule of exportation is legitimate. This will require showing that the rule is truth preserving. To do this, express the rule as a single statement that embodies the rule, and show that that statement is a tautology. Don’t use the rule of exportation in the proof.

4. Discuss the fallacy of begging the question. Your discussion should have 2 components: first, give a concise characterization of the fallacy (you can focus on just the ‘independent’ version if you like, to keep things simple), and illustrate it with an example. You don’t need to get creative with the example, or even make one that is realistic — it can be tough to come up with realistic examples. But just come up with something that illustrates the reasoning pattern even if it’s something that no real person would ever actually use. Second, explain what is bad about begging the question. The second part should discuss both the formal aspects of begging the question, as well as any other aspects necessary to explain what is wrong with it. (Be concise: two or three sentences should suffice for each part.)

5. [10] The following questions refer to Handley et al.’s 2015 “Quality of evidence revealing subtle gender biases in science is in the eye of the beholder”

5a. Briefly state the conclusion of this study. (1-2 sentences)

5b. Briefly describe the experiment and its results.

5c. What, according to the authors, is particularly troubling about the finding?